Download Michelson Morley Experiment

1347
Vol. 4
Indian Journal of Science and Technology
No. 10 (Oct 2011)
ISSN: 0974- 6846
Michelson– Morley experiment: A misconceived & misinterpreted experiment
Mohammad Shafiq Khan
H. No. 49, Al-Farooq Colony, Rawalpora, Srinagar, Kashmir– 190005, India
[email protected]
Abstract
A thorough review of the Michelson–Morley experiment reveals that the experiment had been not only misinterpreted but also
misconceived. Under the theory & methodology adopted by Michelson & Morley the reasons of misconception and
misinterpretation have been found to be: 1. Doppler Effect of light was not taken into account and 2. The motion of the solar
system was not also taken into account. Since this experiment formed the basis of misinterpretation of absence of
luminiferous ether in the space and as the consequence of absence of luminiferous ether the concept of length contraction in
the direction of motion, theories of relativity, space–time concept and big bang theory were adopted. The basis of all these
theories and concepts is challenged. The present article is the detailed and corrected version of the article ‘Ultimate Proof of
Energy Theory of Matter & Cosmology’ Mohammad Shafiq Khan (2010a) necessitated by the article ‘Foundation of Theory of
Everything; Non-living & Living Things’ Mohammad Shafiq Khan (2010b). This article finally explains the Michelson-Morley
experiment.
Keywords: Michelson – Morley Experiment, time-frame, luminiferous ether, recessional velocity, blue-shifting, red-shifting,
anisotropy, Lorentz symmetry
Introduction
‘In what precedes, only the orbital motion of the earth is
In the article Mohammad Shafiq Khan (2010b) it is
considered. If this is combined with the motion of the solar
stated that the article Mohammad Shafiq Khan (2010a)
system, concerning which but little is known with certainty,
should be considered for its contents wherein it was
the result would have to be modified; and it is just possible
suggested that the Michelson–Morley experiment was
that the resultant velocity at the time of the observations was
misinterpreted for concluding the absence of luminiferous
small though the chances are much against it. The
ether as the Doppler Effect was not taken into account. This
experiment will therefore be repeated at intervals of three
article describes that the said experiment had been not only
months, and thus all uncertainty will be avoided’.
misinterpreted but also misconceived to conclude the
A serious lapse had been committed by Michelson in the
absence of luminiferous ether. To understand this article
experiment concluded and reported under article Albert
readers are supposed to have thoroughly studied the articles
Abraham Michelson (1881); which had been aptly pointed
‘The Relative Motion of the Earth and the Luminiferous
out by H. A. Lorentz. This serious lapse could be easily
Ether’ (1881) by Albert Abraham Michelson, ‘On the Relative
understood by below reproduced para of the article
Motion of the Earth and the Luminiferous Ether’(1887) by
Michelson and Edward Morley (1887);
Albert Abraham Michelson & Edward Morley, Mohammad
‘In deducing the formula for the quantity to be measured,
Shafiq Khan (2010b), and ‘Energy Theory of Matter &
the effect of the motion of the earth through the ether on the
Cosmology’ Mohammad Shafiq Khan (2010c).
path of the ray at right angles to this motion was over looked.
The history, background and consequences of
The discussion of this oversight and of the entire experiment
Michelson–Morley experiment are very well-known and as
forms the subject of a very searching analysis by H. A.
such need not be discussed herein. In this article the
Lorentz, who finds that this effect can by no means be
conclusions drawn from ‘null’ result of the said experiment
disregarded. In consequence, the quantity to be measured
are challenged on the same premises on which the
had in fact but one half the value supposed, and as it was
conclusion about the absence of the luminiferous ether was
already barely beyond the limits of errors of experiment, the
drawn. Article Mohammad Shafiq Khan (2010b) describes
conclusion drawn from the result of the experiment might
the foundation of a theory which challenges the physics
well be questioned; since, however, the main portion of the
which evolved during the twentieth century and since the
theory remains unquestioned, it was decided to repeat the
basis of twentieth century physics is the ‘null’ result of
experiment with such modifications as would insure a
Michelson–Morley experiment and the evidence that the said
theoretical result much too large to be masked by
experiment was misconceived and misinterpreted would
experimental error’.
indirectly substantiate the theory put forward under the
Now then the final picture of the experiment; as
article Mohammad Shafiq Khan (2010b).
described by Michelson–Morley; could be represented by the
How Michelson – Morley experiment was Misconceived &
Fig.1. Since readers are supposed to have studied the article
Misinterpreted
Albert Abraham Michelson (1881) and Michelson and
The perusal of the articles Albert Abraham Michelson
Edward Morley (1887) thoroughly as such Fig.1 &
(1881) and Albert Abraham Michelson and Edward Morley
experimental set-up would require no description. However it
(1887) would reveal that only the orbital motion of earth was
be borne in mind that in the calculations which follow it is
considered as rotational motion of the earth and the orbital &
presumed that ether exists in space and the light propagates
recessional motion of the solar system were not considered
in ether with a constant velocity ‘c’ with respect to the ether
for drawing the conclusion. To clarify this fact a para from
at rest. Also the instrument which includes mirrors M1 & M2
the article Albert Abraham Michelson and Edward Morley
and semi-silvered mirror/point of interference are in motion
(1887) is reproduced as follows
with respect to ether with a velocity v.
Review
Indian Society for Education and Environment (iSee)
“Unraveling the truth in experimental science”
http://www.indjst.org
M.S.Khan
Indian J.Sci.Technol.
1348
Vol. 4
Indian Journal of Science and Technology
No. 10 (Oct 2011)
ISSN: 0974- 6846
Dv
Dv

cv cv
2 Dv 2
 2D  2
c  v2
2 Dc 2
 2
c  v2
2D

v2
1 2
c
v2
 2 D(1  2 ) 1
c
v2
 2 D((1  2 )...........(13)
c
 2D 
Let t1 be time required for propagation of light from ‘a’ to
‘b’ and let d1 be the distance the mirror M1 travels during the
time t1 (Since mirror M1 is moving toward the position ‘a’ and
d1 is the distance mirror M1 moves with respect to ether at
rest during the period light pulse reaches the position’b’)
ct 1  D  d 1.............(1)
Since the instrument moves in ether with a velocity v
d 1  vt1.................( )
ct1  D  vt1
D
.........(3)
cv
;
Dv
d1 
.........(4)
cv
ct 2  D  d 2.........(5) ;
d 2  vt 2............(6)
D
...........(7) Hence
cv
;
d2 
Dv
.......(8)
cv
Let ‘d’ be the distance mirror M2 moves during the period
the light propagates from ‘a’ to the mirror M2 and the time be
denoted by t
ct  D  d ..........(9) ;
t
D
c2  v2
d  vt.........(10)
2
.......(11)
d
Dv
.......(1)
c v
;
The distance traversed by the light in the direction of the
earth’s motion to arrive at the point of interference is D-d1 +
D+d2
D  d 1  D  d 2  2D  d 2  d 1
Review
Indian Society for Education and Environment (iSee)
2
2
 D2  d 2
 D2  d 2   D2 

Similarly t2 be time required for propagation of light from
‘b’ to ‘f’ and let d2 be the distance semi-silvered mirror travels
during the time t2 ; d2 is distance traveled by semi-silvered
mirror with respect to ether at rest during the period light
pulse moves from position ‘b’ to ‘f’
Then
2
interference is

t1 
t2 
neglecting the terms of fourth & higher order as Michelson &
Morley had done.
The distance traversed by the light in the perpendicular
direction to the earth’s motion to arrive at the point of
D2 c2
c2  v2
D
v2
1 2
c
D 2v 2
c2  v2
..........(14)

1
 v2  2
  D 1  2 
 c 
1 v2
  D(1 
)...........(15)
2 c2
neglecting the terms of fourth and higher order.
From equation (13) and (15) we deduce that the difference
of the distances traversed by light in the two arms of the
experiment is
D
v2
c2
. Evidently the distance traversed by
light in the arm of the experiment along the direction of
motion of instrument is higher by
D
v2
c2
.
The time taken by the light pulse in traversing the vertical
arm is 2t; so
t  
D
v2
c 1 2
c
“Unraveling the truth in experimental science”
http://www.indjst.org
..............(16)
M.S.Khan
Indian J.Sci.Technol.
1349
Vol. 4
Indian Journal of Science and Technology
No. 10 (Oct 2011)
ISSN: 0974- 6846
The time taken by the light pulse in traversing the
horizontal arm is t1 + t2
D
D

cv cv
Dc
t1  t    2 2
c v
D
t1  t  
..............(17)
v2
c(1  2 )
c
t 1  t  
neglecting the terms of fourth and higher order; we could
write (16) and (17) as
D
1 v2
D
v2
t 
(1 
)....(18) t 1  t  
(1  2 )....(19)
c
2 c2
c
c
;
Evidently the time taken by light pulse in traversing the
horizontal arm is more by
Dv 2
c3
. So far the calculations of
the Michelson–Morley experiment match with the calculations
in this article.
The reason of misconception and misinterpretation of
Michelson–Morley experiment had been that without
measuring the actual distances traversed by the light pulses
in the two arms of the experiment; before the two light pulse
were allowed to interfere; and without measuring the actual
time taken by the light pulse in traversing the two arms of the
experiment the inference was drawn that the time taken by
the light pulse in traversing the two arms of the experiment is
same and also the distances traversed by the light pulse in
traversing the two arms of the experiment is same as the
consequence of the ‘null’ result of the shift of the interference
fringes; when the instrument is revolved through 900 without
considering the Doppler Effect. It needs no over-emphasis
that Doppler Effect had to be taken into consideration before
drawing any conclusion. Now then if it is shown that
notwithstanding the differences in the distances and time
taken by the light pulses in traversing the two arms of the
experiment; before these were allowed to interference; there
had to be no shift of the interference fringe when the
instrument is revolved through 900 after taking the Doppler
Effect into consideration; that should leave no doubt that the
Michelson–Morley experiment was misconceived and
misinterpreted. In what follows is to show that the
experiment was misconceived and misinterpreted which
even an under-graduate student of physics can understand.
Let us consider the propagation of the light pulse in the two
arms of the instrument separately (Fig.2). As the light pulse
moves from ‘a’ (semi – silvered mirror) towards the mirror M1
and by the time it reaches the mirror M1 the mirror moves to
the position ‘b’ at a distance ‘d1’ from the original position of
the Mirror M1. Assuming that there is luminiferous ether and
light propagates at a fixed velocity ‘c’ with respect to the
luminiferous ether. Since light moves with a defined velocity
‘c’ with respect to the ether at rest and since the mirror M 1 is
moving towards the point ‘a’ so the mirror M1 will observe the
Review
Indian Society for Education and Environment (iSee)
light as blue-shifted according to the Doppler Effect. By the
time light pulse reaches mirror M1 the point ‘a’ will shift to the
position ‘g’ which is at a distance ‘D’ from the position ‘b’ of
the mirror M1. As the light pulse is reflected from the mirror
M1 from the position ‘b’ and by the time the light pulse
reaches the point of interference the point ‘a’ reaches the
position ‘f’ at a distance ‘d2’ from the position ‘g’. since the
ether is supposed to be at rest and light moves with respect
to ether with a velocity ‘c’ the point of interference is
receding from the point ‘b’ with a velocity ‘v’ thus according
to the Doppler effect the light will be observed to the redshifted as it reaches the point ‘f’. Let the total number of
waves which the light will have to traverse to reach the point
‘f’ be NH.
NH 
D  d1

BS

D  d

.............(0)
RS
Where  BS is the wavelength of the blue-shifted light due to
the approaching motion of the receiver mirror M1 with the
velocity . . and  RS is the wavelength of the red-shifted
light due to the receding motion of the receiving point (point
of interference) with the velocity ' v ' . Let
the
 o be
wavelength of the same light as observed by the observer
who is at rest with respect to the ether. The Doppler Effect;
as was & is known presently in non-relativistic physics; had
to be taken into account and the change in wave-length is
given as follows:
 

v
c
1
 

............................( 1)
0
BS
.............................( )
v
c
D  d1
D  d
NH 

0
RS
1


0
v
1
c
NH 
D
v
c
Dv
D
cv
1
Dv
cv 

0

0
v
1
c
1
0
v
c
cv
cv
Dc
Dc
NH 
 c 
 c
cv
0
cv
0
D D
D
NH 

  ..................( 3)

0

“Unraveling the truth in experimental science”
http://www.indjst.org
0

0
M.S.Khan
Indian J.Sci.Technol.
1350
Vol. 4
Indian Journal of Science and Technology
M2
In so far as the
propagation of light along
the direction perpendicular
to the direction of motion of
ν
the instrument is concerned,
D
it has been conceived
probably for the first time in
the scientific history of
Michelson–Morley
experiment that a receding
d
d
motion of mirror M2 is
a
f
h
involved while the light
Fig. - 3
pulse propagates form the
point ‘a’ towards the mirror M2 and also the receding motion
is involved when the light pulse is reflected form mirror M2 as
it proceeds towards the point ‘f’; the point of interference
(Fig.3). As the light pulse proceeds from point ‘a’ to the
mirror M2 which is at a distance ‘D’; the light pulse traverses
not the distance ‘D’ but actually traverses the
D
distance
1
2
; which is more than ‘D’. Hence a receding
v
c2
motion is involved while the light pulse traverses from ‘a’ to
the mirror M2 and also during the time the same light pulse is
reflected from the mirror M2 till the light pulse reaches point
‘f’; the point of interference.
Additional distance traversed by the light pulse while
moving from ‘a’ to M2 or M2 to ‘f’
=
D
1
2
=
Accordingly the light pulse, while it traverses in the
arm perpendicular to the direction of the movement of the
instrument, is also red-shifted because of the receding
velocity of
 
Now
VRS

0
1 v2
1 2
2c

VRS
be the
...............(5)
Thus the number of waves which the light will have to
traverse in the vertical arm say Nv
Nv=
Distance traversed
wavelength
Distance traversed is given by equation (14)
2D
1
Nv 
v
c2
Equating


D
Nv  

v2
 1 2
c

v2
c2
0
1 v2
2 c2
(1 
  1 v2
  1
2
 2 c
  0
 







;
2
1v
)
2 c2
to
1
v2
c2
after neglecting the terms
of fourth & higher order.
v2
c 1 2
c
Nv 
v2
c2
 1 v2 
 c  c 1 
2 
 2 c 
neglecting the terms of fourth & higher order.
Velocity of receding
1 v2

...........(4)
2c
Review
Indian Society for Education and Environment (iSee)
D

.................(6)
0
We deduce from equation (23) and (26)
that whatever be the distances traversed by
the light pulses and whatever be the time taken
by the light pulses in traversing the two arms of
the instrument before the light pulses interfere;
v2
the light pulses have to traverse the same
c 1 2
number of waves in the two arms of the
c
instrument. When the instrument is revolved
through 900 the number of waves would remain the same
and as such there could not be any shift in the interference
fringes. Thus when we take Doppler Effect into consideration
there had to be ‘null’ result of the experiment despite the fact
that there is difference in the time taken by the light pulses in
traversing the two arms of the instrument and also despite
the fact there is the difference in the distance traversed by
the light pulses while traversing the two arms of the
instrument according to theory and methodology of
Michelson & Morley. This should be sufficient to show that
Michelson–Morley experiment was misconceived and
misinterpreted to conclude the absence of the luminiferous
v2
1 2
Additional Distance
c
Velocity of receding 

D
Time Period over which the additional distance is traversed
c  c 1
. Thus the wavelength of the light in this
arm of the instrument is red-shifted and let
wavelength of the red-shifted light.
D
=
1 v2
2 c
1
D
ISSN: 0974- 6846
Velocity of receding while the light pulse propagates from
the mirror M2 towards the point ‘f’ is the same.
D
Time period over which the additional distance is traversed
No. 10 (Oct 2011)
D
“Unraveling the truth in experimental science”
http://www.indjst.org
M.S.Khan
Indian J.Sci.Technol.
1351
Vol. 4
Indian Journal of Science and Technology
ether. However, Fig.4 & Fig. 5 and calculations would reveal
that the result of the experiment would remain the same
when the movement of the instrument with respect to the
luminiferous ether is reversed.
Dv
.......(7)
cv
;
d 1  vt 1 
d   vt  
Dv
.......( 
cv
The distance traversed by light pulse form point ‘a’ to ‘b’
is D+d1 while the light pulse is red-shifted as the mirror M1 is
moving away and similarly the distance traversed by the light
pulse after it is reflected is D-d2 and during this travel light
pulse is blue-shifted. Thus number of waves which the light
pulse has to traverse in this arm of the instrument .
NH 
D  d1
D d
RS
D

ISSN: 0974- 6846
There is one more aspect which is being considered
probably again for the first time in the history of MichelsonMorley experiment which needs to be taken into account
to finally decides upon the Michelson–Morley experiment.
This aspect concerns the distances traversed by light
pulses in the horizontal and vertical arms from the semisilvered mirror to the point of the interference. The
horizontal light pulse travels the distance of d1+d2 from the
original position of the semi-silvered mirror when it interferes
with the vertical light pulse; whereas the vertical pulse
travels the (horizontal) distance of 2d from the original
position of the semi-silvered mirror when it interferes with the
vertical light pulse.
d 1  d   vt1  vt 
Dv
Dv
 Dvc

 2
........(30)
c  v c  v c  v2
 Dv
d 
....................(31)
c2  v2
d1  d  
Equation (30) & (31) could be written also as


 




Dv
Dv 
 D
  D

cv 
cv 
NH  
0   0 


v  
v 
 1
  1

c  
c 

Nv 


No. 10 (Oct 2011)
BS
d1  d  
d  
 Dv

c
Dv
c
1
...........(3)
v2
1 2
c
1
................(33)
v2
1 2
c
Evidently d 1  d   d


 Dv  1
1
d 1  d   d 

2
c 
v
v2
1

1 2

c2
c

2
2
Dv
v
1v

(1  2  1 
)
c
2 c2
c
....................(9)
0






neglecting the terms of fourth & higher order.
d 1  d   d  D
v3
c3
This is the ultimate dependence of the shift of
interference fringes on the velocity of the earth. Now
according to the calculations of the Michelson & Morley the
Here also the formulae (24) (25) and (26) would apply
Nv 
D

0
Hence even then there has to be the ‘null’ result of the
experiment. This condition will arise when the experiment is
repeated after six months when the direction of motion of the
instrument is reversed due to the position of the earth.
Review
Indian Society for Education and Environment (iSee)
difference of distances is
v2
D 2
c
which corresponds to the
4
 .04 of the distance between interference fringes of
100
v3
the yellow light but actually the difference is D 3 which
c
“Unraveling the truth in experimental science”
http://www.indjst.org
M.S.Khan
Indian J.Sci.Technol.
1352
Vol. 4
Indian Journal of Science and Technology
would correspond to
4
 .000004 of the distance
100000
between interference fringes which in no case could have
been detected at the time. Detection of shift in the
interference fringes to this extent is being detected presently
with highly accurate and sophisticated Michelson–Morley
experimental instruments. Factually this fringe shift is
negligible and we may safely conclude that the ‘null’ result of
the Michelson-Morley experiment is actually the evidence of
the existence of the luminiferous ether.
Recall equation (23) and (26) the number of
wavelengths which the two light pulses travel before they
interfere is independent of the velocity of the earth and these
only depend on the wavelength of the light and the lengths of
the arms. So the future experiments like Kennedy-Thordike
experiment (1932) and later experiments using lasers and
masers which have been misinterpreted as the proof of the
theory of relativity; actually confirm the existence of the
luminiferous ether.
Recall equations (14) and (16)
The distance traversed and time taken by the light pulse in
the vertical arm is
D
Distance =
v2
1 2
c
D
Time  t 
c 1
....(34)
;
v2
c2
...(35)
D
v2
1 2
c
Time  t 1  t  
D
 v2 
c 1  2 
 c 
Since the ‘null’ result of the Michelson–Morley experiment
was misinterpreted to conclude that there is no difference of
time or distances while the light pulse traverses in the two
arms of the experiment, it was proposed by the Lorentz &
FitzGerald that the experiment could be explained only if we
assume that there is length contraction in the direction of
motion
1
by a factor of
v2
c2
. Thus in the above equations
(horizontal arm distance traversed and time taken) we have
to replace D by
Distance =
v2
D 1 2
c
D
1
2
then these equations would be;
Time  t 1  t  
v
c2
Review
Indian Society for Education and Environment (iSee)
D
c 1
ISSN: 0974- 6846
These equations now equate with equations (34) and (35)
Now if we assume that there is no luminiferous ether and
the velocity of light is ‘c’ irrespective of the motion of the
source and the observer. Then if 2D is the distance light
pulse has to traverse with the contraction already included,
then actual distance between the point ‘a’ and the mirror
M 1 is
D
v2
1 2
c
. Thus the actual distance traversed by the
light pulse in the horizontal arm is
D
the time taken is
v2
c 1 2
c
D
v2
1 2
c
which exactly matches with
1
v2
c2
of space contraction and
time dilation. The solution arrived by Voigt later on became
the Lorentz transformation on the basis of the ‘null’ result of
the Michelson–Morley experiment wherein it was concluded
that there is no luminiferous ether and accordingly the
velocity of light had to be treated as constant ‘c’ irrespective
of the relative motion of the source and the observer. In
absence of the luminiferous ether; for which the
misinterpretation of Michelson–Morley experiment served as
the basis; there was no alternative but to adopt the space
contraction and invariability of velocity of light irrespective of
the relative motion of the source and the observer as the
intrinsic characteristic of light. When these two concepts are
applied to the transformation between two coordinate
systems in uniform relative motion; the outcome is the time
dilation. To demonstrate this let us consider the Galilean
transformation between two coordinate systems in uniform
relative motion; we will consider only the transformation of
the space coordinates
x '  x  vt
Let the time of the two coordinate systems be t and t’
Adopting the space-contraction
x '   ( x  vt )................(36)
Adopting the invariability of velocity of light
and x  ct
Equation (36) could now be written as
x '  ct '
ct '   (ct  vt )
2
v
c2
and accordingly
equation (34) and (35). This being one of the strange
coincides and the second coincidence was that Woldemar
Voigt in the same year i.e. 1887 proved mathematically that
the D’Alembert’s wave-equation of space and time
dependent scalar wave function is not invariant under
Galilean transformation and he arrived at a transformation in
which there is a factor of
Similarly recall the equations (13) and (19) which gives the
distance traversed by the light pulse and time taken by the
light pulse in the horizontal arm
Distance =
No. 10 (Oct 2011)
v
t '   (1  )t
c
“Unraveling the truth in experimental science”
http://www.indjst.org
or
t '   (t 
v
x)......(37)
c2
M.S.Khan
Indian J.Sci.Technol.
1353
Vol. 4
Indian Journal of Science and Technology
Thus time dilation is the outcome of the adoption of the
space contraction and the invariability of velocity of light as
Woldemear Voigt’s mathematical solution had predicted.
But in absence of the luminiferous ether the concepts of
space contraction in the direction of motion and invariability
of velocity of light as the intrinsic characteristic of light were
adopted despite these concepts were illogical, irrational and
against all known science even at the time.
Logically, the experimental measurement of refractive
indices of different transparent materials loudly and clearly
reveals that the velocity of light does depend upon the
medium and cannot be intrinsic characteristic of light.
Let there be source of light O and there be three
observers A, B and C with the instruments for measurement
of wavelength of the light they receive. Without any
reference to the existence of the luminiferous ether, the
three observers be such that the observer A is in receding
motion with respect to the source of light O with a velocity ‘v’,
the observer B be at rest with respect to the source of light O
and the observer C be in approaching motion with respect to
the source of light O with a velocity v. Now according to the
Lorentz transformation the space between O & A and O & C
is contracted whereas there is no effect on the space
between O & B. This suggested that almost the same space
is contracted and the same space, between O & B, is not
contracted. This evidently is illogical and seems to be absurd
on the face of it.
Fig.6
O
A
V
B
C
V
Keeping in view the Fig.6 consider the very well known
experimentally and theoretically studied Doppler Effect. It
should be borne in mind that Hubble observations are simply
the experimental measurements of the Doppler Effect. Now
according to the Lorentz transformation the space is
contracted when the observer is approaching or receding. In
classical physics as well as in the modern physics including
relativistic physics light is known to be a wave phenomenon.
Since space is contracted due to the approaching or
receding motion of the observer with respect to the source of
light so the waves should get contracted and thus the
wavelength should be reduced. Hence according to the
Lorentz transformation light should be blue-shifted whether
the observer is approaching or receding the source. This is
against all the experimental observations of the Doppler
Effect especially Hubble observations wherein only redshifting have been observed; if we presume that red-shifting
is not due to expansion of space which shall be shown in this
article. Thus the concept of space contraction in the direction
of motion cannot be correct.
Consider the same Fig.6. There is the same source of
light, same space and same types of instruments with
observers A, B & C and the only difference is the relative
Review
Indian Society for Education and Environment (iSee)
No. 10 (Oct 2011)
ISSN: 0974- 6846
motion of the observers with respect to the source. It will be
illogical and irrational to even imagine that the difference in
the relative motion of the instruments with respect to the
source could change the wavelength of the light being
emitted by the source or the relative motion of the source
and the observers could affect the space. There has to be
something intrinsic to the instruments which changes due to
the relative motion of the instruments and the source of light
as the result of which the wavelength of the same light is
observed to be different. That is exactly what the theory put
forward in the article Michelson and Edward Morley (1887)
has established. Due to the relative motion of the source and
the observer; which would cause difference in motion of the
observer with respect to the ether; which being the cause of
the difference in the time frame of the observer.
Michelson and Morley in no case, should have ignored
the motion of the solar system about which little was known
at that time, as honestly conceded by them. Thus even the
misconceived and misinterpreted conclusions of the
Michelson–Morley experiment had to be provisional till
everything about the motion of the solar system was known.
Michelson and Morley had decided that the effects of the
motion of the solar system could be neglected if the
experiment is repeated at the intervals of three months and if
there is no effect on the result of the experiment. But this
decision of Michelson & Morley; as will be explained; is one
of the fundamental errors in the theory & methodology
adopted. A thorough review of the Michelson–Morley
experiment would not be complete if we do not consider the
motion of the solar system. As established in the article
Michelson and Edward Morley (1887) and also proved in this
article that the circular motion of the earth could not result in
any considerable shift of the interference fringes when the
instrument is revolved by 900.
Now let us consider the situation when the instrument is
aligned in the direction of the motion of the solar system.
The formulae and the principles will remain the same and
the mathematical deductions would also remain the same
when we considered the orbital motion of the earth. As we
have seen that according to the Michelson & Morley the
difference of the distances traversed by the light pulses
before they interfere is
v2
D 2
c
whereas the actual difference
of the distances as worked out in this article is
D
v3
c3
.
According to the calculations of the Michelson & Morley
there should have been the shift of 0.04 interference fringes
of the yellow light when the instrument is revolved by 900
whereas actually according to this article there could be the
shift of .000004 interference fringes. But since the solar
system is by now known to be revolving around the centre of
the galaxy with an orbital velocity of about 7.3 times than the
orbital velocity of the earth around the sun. Thus the shift of
the interference fringes when the instrument is aligned in the
direction of the motion of the solar system would be (7.3) 3 =
390 times that what we have worked out while we have
considered the orbital motion of the earth. Thus the highest
shift of the interference fringes could be 0.0015 (for yellow
“Unraveling the truth in experimental science”
http://www.indjst.org
M.S.Khan
Indian J.Sci.Technol.
1354
Vol. 4
Indian Journal of Science and Technology
No. 10 (Oct 2011)
ISSN: 0974- 6846
light) when the instrument is aligned in the direction of the
v
motion of the solar system. Hence the shift of the
D 
c c
interference fringes would vary from 0.000004 to 0.0015 (for
Michelson & Morley and thesis of this article is
yellow light) depending upon the alignment of the instrument
v v
D 
with respect to the motion of solar system at the time of the
c
experiment. Thus the result of the experiment would depend
where ν is the velocity of the earth. Thus this ratio is 10,000.
upon the position of the place on earth where the experiment
This has to be the highest possible ratio. Now consider the
is undertaken.
position when the instrument is aligned along the motion of
The Michelson–Morley experiment has been repeated
the solar system. In this case the difference of distances
since 1887 and every time there had been improvement in
traversed by the light pulse in the two arms of the
the quality of light (anisotropy) and instrumentation but the
results fall within the range as predicted in this article by a
vs 3
experiment is  D 3 vs is the velocity of solar system )
strange coincidence. In the absence of luminiferous ether,
c
these studies are made under the context of violation of the
whereas according the Michelson & Morley the difference is
Lorentz symmetry and anisotropy of space.
In the article Mohammad Shafiq Khan (2010a) the same
v
mistake was committed which Michelson had committed in
again the same  D  (ν is the velocity of earth). Thus this
c
his explanation of the 1881 experiment. Besides I had

arrived at the same conclusion as in this article; but with the
vc
help of very crude calculations wherein d, d1 and d2 were not
ratio would be
. Since the solar system is known to be
vs 3
taken into account but only the Doppler Effect was taken into
account.
revolving around the centre of the galaxy with an orbital
Finally I could not think of any other simpler way of
velocity which is about 7.3 times the orbital velocity of the
showing
that
Michelson–Morley
experiment
was
c
10000
earth, hence the ratio would be

 5 .
misconceived and misinterpreted which even an under
(7.3) c
390
graduate student of physics can understand without any
difficulty.
Thus the ratio would vary from 25 to 10,000 depending upon
Experimental & Theoretical Evidences
the position of the place of the experiment on the earth.
Even under the methodology & theory adopted by Michelson
Following table gives this ratio in respects of Michelson& Morley; which will be shown to be incorrect there are
Morley experiments conducted up to 1930.
sufficient
experimental
&
Table I (the erratic experiments of Miller has been excluded and only the easily available
theoretical evidences which
experimental results on internet have been quoted)
favour the thesis put forward
Name
Location
Year
Fringe
Fringe
Ratio
in this article and which also
shift
shift
confirm that Michelson-Morley
expected measured
experiment was misconceived
Michelson and Morley
Cleveland
1887
0.4
< 0.02
40
and misinterpreted. Since the
or ≤ 0,01
difference
of
distances
traversed by light pulse in two
Morley and Miller
Cleveland
1902–1904
1.13
≤ 0.015
80
arms of Michelson–Morley
Miller
Cleveland
1923–1924
1.12
≤ 0.03
40
instrument, if we presume
luminiferous ether in the
Miller (sun light)
Cleveland
1924
1.12
≤ 0.014
80
space according to the
Michelson & Morley is
v
D 
c
and when the instrument is
revolved by 900 there should
be shift in the interference
fringes by
D
v
c
Kennedy
Piccard & Stahel
Pasadena/Mt. Wilson
with a Balloon
1926
1926
0.07
0.13
≤ 0.002
≤ 0.006
35
20
Piccard & Stahel
Piccard & Stahel
Brussels
Rigi
1927
1927
0.13
0.13
≤ 0.0002
≤ 0.0003
185
185
Michelson et al.
Joos
Mt. Wilson
Jena
1929
1930
0.9
0.75
≤ 0.01
≤ 0.002
90
375
fringes.
Now according to the thesis of this article there could be shift
in the interference fringes to the extent of
D
v3
c3
. Now
when we presume that the instrument is aligned in the plane
which is perpendicular to the movement of solar system;
then we have to consider only the orbital motion of the earth.
Thus the ratio of expected shift of interference fringes under
Review
Indian Society for Education and Environment (iSee)
The perusal of the Table 1 would reveal that the thesis of
this article is confirmed by the experimentation spread over
about half a century.
Since last a few decades; in absence of the luminiferous
ether; these studies are made under the context of
misconceived anisotropy of space. The experimental results
under the anisotropy of space are also consistent with the
thesis of this article. Working out the exact correlation
between the experimental results of experiments conducted
under anisotropy of space is irrelevant and beyond the
scope of this article. However the misconceived anisotropy
“Unraveling the truth in experimental science”
http://www.indjst.org
M.S.Khan
Indian J.Sci.Technol.
1355
Vol. 4
Indian Journal of Science and Technology
of space has to be proportional to
v
c
which is of the order

of 10
which; coincidently; being the experimental
observations. This should be sufficient experimental
evidence for misconception & misinterpretation of
Michelson-Morley experiment and existence of luminiferous
ether under the methodology & theory adopted by Michelson
& Morley.
Final explanation of Michelson experiment
Under the theory & methodology adopted by Michelson
& Morley the Doppler Effect had to be taken into account the
way non-relativistic Doppler Effect was and is presently
known. Secondly the motion of the solar system also had to
be taken into account.
In the article Mohammad Shafiq Khan (2010b) a
transformation was derived between the ether at rest frame
of reference and the reference frame which is in any uniform
motion with respect to former frame of reference. Under that
transformation there is absolutely no effect on any aspect of
light/radiation when the moving reference frame is in uniform
circular motion without any component of receding or
approaching motion. Firstly Michelson and Morley should not
have converted the orbital motion of earth into linear motion
and worked out the calculations on that basis. This is basis
of all the confusion created by Michelson-Morley experiment
and this is the fundamental error in the theory &
methodology of Michelson & Morley.
If we assume that sun is in the galaxy whose centre
coincides with the centre of the universe and has no
recessional component for the purpose of simplicity of
explanation. The transformation derived in the article
Mohammad Shafiq Khan (2010b) is
r '  r  vt '
t'  t
Where

1
cˆ.v
1
c
Now for the circular motion the condition that t’=t=0 and the
origins of two coordinate systems coincide cannot be
applicable; hence for such the coordinate systems the
transformation would be
r '  r  R  vt ' & t '   t
R being the radius of the coordinate system in circular
motion.
Since for circular motion cˆ.v  0 ; as ĉ is the unit
directional vector of light; source of which is at the origin of
ether at rest frame of reference.
Hence the transformation would be
r '  r  R  vt ' & t '  t
Since the time-frame of the two coordinate systems is the
same and as explained in article Mohammad Shafiq Khan
(2010b) [4] no Doppler Effect would be called into play. For
such circular motions we could for all practical purposes and
for all calculations treat the ether at rest. Since the vertical
as well the horizontal arms of the Michelson-Morley
instrument have the same angular motion; Michelson &
Morley should not have assigned uniform linear motion to
Review
Indian Society for Education and Environment (iSee)
No. 10 (Oct 2011)
ISSN: 0974- 6846
the instrument. This is true about the rotational motion of the
earth also if the sun & the galaxy had no recessional motion.
But since the solar system & the galaxy (of which sun is one
the stars) are having the circular motion as well as
recessional motion. For the component of the circular motion
of the solar system we could safely assume ether to be at
rest. The calculations done in this article are applicable to
the recessional velocity of the solar system rather than the
motion of the earth. It should be borne in mind that since the
time-frame of all the components of the instrument and the
earth is the same; hence though Doppler Effect will be called
into play but it will not be detectable. But the velocity which is
to be considered is the resultant recessional velocity of the
solar system) & the galaxy (of which the sun is of the stars.
Thus the results of the Michelson-Morley experiment which
presently are being found with highly sophisticated
instrumentation are concerning the resultant recessional
velocity of the solar system & the galaxy (of which the sun is
of the stars; which vary depending upon the position of the
experiment on the earth and the alignment of the instrument
with respect to the direction of the resultant recessional
velocity.
The most important theoretical evidence in favour of the
thesis of this article would be the invariance of the waveequation in the ether at rest frame of reference and any other
frame of reference which is in uniform motion with respect to
the ether at rest frame of reference. The wave-equation in
the ether at rest frame of reference is
 
c   
t


In the article Mohammad Shafiq Khan (2010b) we have
derived the transformation between two coordinate systems;
(in spherical polar coordinates) one of which is at rest with
respect to the ether at rest frame of reference and the other
is moving with velocity v when the origins of the two
coordinates are
transformation is
coinciding
at
t t'o
.
The
r '  r  vt '...........(38)
t '   t.................(39)
Where

1
...........(40)
cˆ.v
1
c
ĉ being the unit directional vector of light, source of which is
at the origin of the ether at rest frame of reference.
Evidently cˆ.v is the recessional or approaching velocity of
the reference frame. The spherical polar coordination have
been adopted for derivation of transformation between the
two coordinate systems in relative uniform motion (one of
which is the absolute reference frame of ether at rest)
because this is the most suitable coordinate system which
describes the motion of the celestial objects. The
transformation could be simply applied in two dimensions
which in no case would be over-simplification. Assuming the
conditions of
“Unraveling the truth in experimental science”
http://www.indjst.org
r  0,0    1800
and
0    3600
for
M.S.Khan
Indian J.Sci.Technol.
1356
Vol. 4
Indian Journal of Science and Technology
the radial coordinate, polar angle and azimuth angle
respectively. The moving reference frame could be
described in the spherical polar coordinates by assuming
polar angle  = 00 wherein only radial coordinate r and
azimuth angle  are variables. Now Laplacian in spherical
polar coordinates is
 
No. 10 (Oct 2011)
ISSN: 0974- 6846
c 2  2 2c 2  2
 2


 2 r 2  2 r r  2 t 2
c2
 2
2c 2  2
 2


(r ) 2  r r (t ) 2
1   
1


1

(r
) 
(sin 
)  
 2 2c 2   2

r r
r r sin  
 r sin    c 2

 2
2
r '
Since 
Hence
r ' r '
 2
c 2  '2   2
t '
 0
1   
(r
)
r  r
r
  
Thus
   
r
r r
 
Thus wave equation in two dimensions with
written as
c    c 
 0
could be
  c    

  ........(41)
r r
r 
t
Equation (38) could be written as after multiplying both sides
by ĉ
cˆ.r  cˆ.r  cˆ.v .t '
r '  r  cˆ.v .t '
r '  r  cˆ.v .t
For any point in space which is observed with the help of
light/radiation
r  ct so r  ct
r '  r  cˆ.v

c
r


 cˆ.v
1 
r '  1 
.
 r
c 1  cˆ.v 

c 

r '  r and also r '   r
Dividing both sides of equation (41) by
Review
Indian Society for Education and Environment (iSee)
2
t '
This should show that the wave-equation is invariant under
the transformation derived in the article Mohammad Shafiq
Khan (2010b) wherein the luminiferous ether is supposed to
be present in the space. In the article Mohammad Shafiq
Khan (2010b) the value of  was derived when the same
transformation was adopted and applied such that the waveequation is invariant. For those under-graduate students of
physics who do not understand the invariance of the waveequation of the wave-motion of light/radiation under a
transformation to a moving coordinate system, this means
that velocity of light is constant with respect to the moving
coordinate system or reference frame irrespective of its
motion with respect to the absolute reference frame of ether
at rest.
Since for the transformation between ether at rest frame
of reference and the reference frame having circular motion
would give r '  r and t '  t ; evidently the waveequation is invariant under such a transformation. Readers
have to bear in mind that in all moving reference frames the
observed velocity of light is constant in the time frame of the
moving reference frames and the time frame of the moving
reference frames would depend on the net recessional
velocity of the moving reference frames.
Discussion
Voigt, Lorentz and Einstein did not realize that there
could be any other transformation which does not involve
any space contraction and under which wave-equation could
be invariant. It has been shown that Michelson-Morley
experiment was misconceived and misinterpreted. With
ether in space, the main task being the derivation of the
transformation between two reference frames; one of which
has to be the absolute reference of ether at rest and other
reference frame being in uniform motion with respect to the
ether at rest frame of reference; and secondly to show that
the velocity of light/radiation is constant irrespective of the
relative motion of the source and the observer. These tasks
have been accomplished in the article Mohammad Shafiq
Khan (2010b).
Michelson-Morley experiment was considered as the
experimental proof of length contraction of space in the
direction of motion and this coupled with the invariability of
velocity of light/radiation irrespective of relative motion of
source and the observer as the reason of time dilation which
subsequently lead to the space-time concept, theories of
relativity and big bang theory. Having shown that MichelsonMorley experiment is in fact experimental evidence of the
“Unraveling the truth in experimental science”
http://www.indjst.org
M.S.Khan
Indian J.Sci.Technol.
1357
Vol. 4
Indian Journal of Science and Technology
existence of ether the simple conclusions are that concept of
space-contraction in the direction of motion, space-time
concept, theories of relativity and big bang theory cannot be
correct.
This article and Mohammad Shafiq Khan (2010b) are
unique in the sense that these articles justify the Doppler
Effect & Hubble observation and show that space is absolute
as there is not a single direct experimental evidence of
space contraction. Secondly the main evidence of space
expansion is the Hubble observations of red-shifting of the
visible spectrum of the light from the galaxies. Since the time
frame of the receding observer (receding with respect to the
ether at rest frame of reference) is slower than the absolute
frame of reference of ether at rest accordingly the observer
will observe the wave phenomenon of the light/radiation on
its time frame and the observed frequency of the wave
phenomenon will be reduced and since light/radiation is
observed to have a constant velocity ‘c’ with respect to the
observer; hence the wave length of the light/radiation will be
observed to be increased (red-shifted) depending upon the
receding velocity of the observer. Conversely wave-length of
the light/radiation will be observed to be reduced (blueshifted) due to the approaching motion of the observer. In
the article Mohammad Shafiq Khan (2010b) it has been
shown that in nature galaxies and stars have only the
receding motion with respect to each other; hence this
explains the red-shifting of the visible spectrum of the light
as observed by Hubble.
With the help of thesis put forward under this article and
the theory put forward under article Mohammad Shafiq Khan
(2010b) it will be a very simple proposition to show that the
conclusions drawn from Sagnac experiment are also
misconceived and misinterpreted.
As described in the article Mohammad Shafiq Khan
(2010b) once the existence of luminiferous ether is adopted
everything
could
be
logically,
scientifically
and
mathematically explained. The secrets of state of existence
of space, time, matter, radiation and that of interactions in
nature are contained in the luminiferous ether and when we
adopt the existence of luminiferous ether all secrets unfold
which stand described in the article Mohammad Shafiq Khan
(2010b).
The invariability of velocity of light irrespective of the
relative motion of the source and the observer as the
intrinsic characteristic of light is simply a preposterous axiom
in absence of the luminiferous ether & difference of time
frames of
Cosmologically in nature the motion of the stars and
galaxies are spiral motions with the outward recessional
component of the motion for reasons already explained in
article Mohammad Shafiq Khan (2010b).
Conclusion
The article shows that Michelson-Morley experiment
was misconceived and misinterpreted to conclude the
absence of the luminiferous ether. In absence of the
luminiferous either, Michelson-Morley experiment cannot be
explained without introducing the contraction of space in the
direction of motion. Contraction of space in the direction of
motion coupled with the invariability of velocity of light
irrespective of the relative motion of the source and the
Review
Indian Society for Education and Environment (iSee)
No. 10 (Oct 2011)
ISSN: 0974- 6846
observer leads to the time dilation and interdependence of
space and time - in short space-time concept. Thus this
article shows that space contraction in the direction of
motion & space-time concept and so theories of relativity, big
bang theory and every science and theory based on these
concepts cannot be correct. This article confirms the
existence of the luminiferous ether; the physical
characteristics of which are described in the article
Mohammad Shafiq Khan (2010b). The alternative state of
existence of space, time, matter, radiation and luminiferous
ether is described in the article Mohammad Shafiq Khan
(2010b). The humanity was deceived by denying the
existence of ether in the space which is visible to even a
layman. If during the night anybody stands near an electric
lamp with the filament and stresses the muscles of the eye;
he would see the shining ether around the lamp.
The concepts and theories based on the space-time
concept and contraction of space in the direction of motion
have resulted in the evolution of the physics in the twentieth
century which fundamentally cannot be correct. The physics
so evolved has been taken too far; as far as to deny the
existence of God. The alternative theistic state of existence
of space, time, matter, radiation, luminiferous ether and the
nature of the interactions in nature is described in the article
Mohammad Shafiq Khan (2010b). This article together with
articles Mohammad Shafiq Khan (2010b), Mohammad
Shafiq Khan (2010c) and ‘Theory of Origin & Phenomenon
of Life’ by Mohammad Shafiq Khan (2010d) are the scientific
evidences against the philosophy of materialism; which
philosophy has been adopted by the mankind for science;
both physical and biological sciences; social, political and
individual life since last about one and a half centuries.
Acknowledgement
I am thankful to Mir Faizal for being in constant touch
and for fruitful discussions during the preparation of this
article. I am also thankful to N. Gajendran for the
encouragement for pursuing this research.
References
1. Albert Abraham Michelson (1881) The relative motion of
the Earth and the luminiferous ether. Am. J. Sci. 22,
120-129.
Available
on
www.archive.org/
details/americanjournal62unkngoog
2. Albert Abraham Michelson and Edward Morley (1887)
On the relative motion of the Earth and the luminiferous
ether. Am. J. Sci. 34 (203): 333-345. Available on
www.aip.org/history/exhibits/gap/ PDF/michelson.pdf
3. Mohammad Shafiq Khan (2010a) Ultimate proof of
energy theory of matter & cosmology. Indian J. Sci.
Technol. 3 (8), 948-954. Available on www.indjst.org
4. Mohammad Shafiq Khan (2010b) Foundation of theory
of everything: Non-living things and living things. Indian
J. Sci. Technol. 3 (9), 955-981. Available on
www.indjst.org
5. Mohammad Shafiq Khan (2010c) Energy theory of
matter & cosmology. Indian J. Sci. Technol. 3 (8) 943947. Available on www.indjst.org
6. Mohammad Shafiq Khan (2010d) Theory of origin &
phenomenon of life. Indian J. Sci. Technol. 3 (8), 937942. Available on www.indjst.org.
“Unraveling the truth in experimental science”
http://www.indjst.org
M.S.Khan
Indian J.Sci.Technol.